is the ath partial derivative in curvilinear coordinates, Ac a vector and êc a basis vector.
because that resolves to (after many headaches, deriving the derivatives of basis vectors and general cursing):
where ha would be the Lamé-coefficients of the specific basis. This is the expression for the gradient of a vector-field, not a scalar field, which should not come as a surprise of course, since (Acêc) is a vector.
Should not come as a surprise. Surprised the hell out of me, though.
Apparently I have nearly managed to forget everything I ever learned about vector and tensor calculus - so I know what I will be doing the next couple of days...
Edit: Formulas generated via the excellent Texify webpage. If you can't see any, then Texify is dead or down - sorry about that!
Edit the second: Put in the formulas as images, so everybody can see them, even if Texify is acting up - thanks Stephanie for pointing that out!.